Vibrational Frequency of Weak-coupling Impurity Bound Polaron in Quantum Rods

The Hamiltonian of a quantum rods with an ellipsoidal boundary is given after a coordinate transformation which can transform the boundary into a spherical one.The properties of the weak -coupling impurity bound polaron in a quantum rod in a three-dimensional anisotropic harmonic potential are studied by using the linear combination operator and the unitary transformation methods.The relations of the vibrational frequency of weak-coupling impurity bound polaron in a quantum rod with the.Coulomb bound potential and the aspect ratio of the ellipsoid and the mean number of phonons with the electron-phonon coupling strength and the aspect ratio of the ellipsoid were derived.Numerical calculations are performed and the results show that the vibrational frequency will increase with increasing the Coulomb bound potential.The vibrational frequency is increasing functions of the aspect ratio of the ellipsoid when e′l,whereas it is decreasing functions of one when e′l.Whene'=1,the vibrational frequency have a minimum value.The mean number of phonons is increasing functions of the electron-phonon coupling strength whereas it is decreasing functions of the aspect ratio of the ellipsoid.